Problem: Solve for $a$. $-\dfrac14a-4=\dfrac74a-3$ $a=$
Explanation: We need to manipulate the equation to get $ a $ by itself. $\begin{aligned} -\dfrac14a-4&=\dfrac74a-3 \\\\ -\dfrac14a-4 {-\dfrac74a} &= \dfrac74a-3{-\dfrac74a} &&\gray{\text{Subtract} \dfrac74a \text{ from each side.}}\\\\ -2a-4&=-3 &&\gray{\text{Combine like terms.}}\\\\ -2a-4{+4} &= -3{+4} &&\gray{\text{Add 4 to each side.}}\\\\ -2a &=1 &&\gray{\text{Combine like terms.}}\\\\ \dfrac{-2a}{{-2}} &= \dfrac{1}{{-2}} &&\gray{\text{Divide each side by -2.}}\\\\ a &= {-\dfrac12} &&\gray{\text{Simplify.}}\\\\ \end{aligned}$ The answer: $ a= {-\dfrac12 }~~~~~~~~$ [Let's check our work!]